Materials design has largely expanded to multiple compositions, which requires the mixing of an increasing number of elements. In this joint Focus issue with Nature Materials, we take a closer look at the role of computational methods for guiding exploration within such vast chemical spaces.

Machine learning models have been widely applied to boost the computational efficiency of searching vast chemical space of compositionally complex materials. This Perspective summarizes the recent developments and proposes future opportunities, such as the physics-informed machine learning models.

Complex materials offer promises for exotic materials properties that enable novel applications. Nevertheless, there are numerous computational challenges for a rational design of defects in such materials, thus inspiring opportunities for developing advanced defect models.

The computational characterization of short-range order in compositionally complex materials relies on effective interatomic potentials. In this Review, challenges and opportunities in developing advanced potentials for such systems are discussed, with a focus on machine learning-based potentials.

A manifold learning method called T-PHATE is developed for high-dimensional time-series data. T-PHATE is applied to brain data (functional magnetic resonance imaging) where it faithfully denoises signals and unveils latent brain-state trajectories which correspond with cognitive processing.

A computational method is proposed to generate the full-scale dataset of the tridimensional position and connectivity of neurons in the CA1 region of the human hippocampus starting from high-resolution microscopy images and experimental data.

The study shows that scale-specific oscillations and scale-free neuronal avalanches in resting brains co-exist in the simplest model of an adaptive neural network close to a non-equilibrium critical point at the onset of self-sustained oscillations.

A biasing energy derived from the uncertainty of a neural network ensemble modifies the potential energy surface in molecular dynamics simulations to rapidly discover under-represented structural regions that meaningfully augment the training data set.

A topological data analysis-driven machine learning model for guiding protein engineering is proposed, complementing protein sequence and structure embeddings when navigating the fitness landscape.

The concept of evolving scattering networks is proposed for material design in wave physics. The concept has the potential to enable network-based material classification, microstructure screening and the design of stealthy hyperuniformity with superdense phases.

Materials design has largely expanded to multiple compositions, which requires the mixing of an increasing number of elements. In this joint Focus issue with Nature Materials, we take a closer look at the role of computational methods for guiding exploration within such vast chemical spaces.

Dr Núria López-Bigas, ICREA Research Professor and group leader in biomedical genomics at the Institute for Research in Biomedicine, discusses with Nature Computational Science about her research on cancer genomics.